Solve the number problem below.

Question

If a number is added to the numerator of 2/5 and the same number is subtracted from the denominator, the result is 6. Find the number

Answer 1

Rick, try translating the words into algebraic expressions first.

Let x be “the number”

Translate the first clause “if a number is added to the numerator of 2/5”. First, what is the numerator of 2/5?

it’s 2

if x is added to 2, what does that look like?

(x+2)/5

 

Next Translate “and the same number is subtracted from the denominator”.

What is the denominator?

it’s 5

if x is subtracted from the denominator, what does that look like?

(x+2)/(5-x)

Finally, Translate “the result is 6” into “=6”

 

here is the equation

(x+2)/(5-x) = 6

 

i assume that you know how to solve this, but for the younger students reading this, here’s a hint:

multiply both sides by (5-x)

 

you get (x+2) = 6(5-x)

 

solve for x, and there’s your answer.